Question: Jessica is 3 times as old as Omar. Twenty years ago, Jessica was 7 times as old as Omar. How old is Jessica now?
Solution: We can use the given information to write down two equations that describe the ages of Jessica and Omar. Let Jessica's current age be $j$ and Omar's current age be $o$ The information in the first sentence can be expressed in the following equation: $j = 3o$ Twenty years ago, Jessica was $j - 20$ years old, and Omar was $o - 20$ years old. The information in the second sentence can be expressed in the following equation: $j - 20 = 7(o - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to solve our first equation for $o$ and substitute it into our second equation. Solving our first equation for $o$ , we get: $o = j / 3$ . Substituting this into our second equation, we get: $j - 20 = 7($ $(j / 3)$ $- 20)$ which combines the information about $j$ from both of our original equations. Simplifying the right side of this equation, we get: $j - 20 = \dfrac{7}{3} j - 140$ Solving for $j$ , we get: $\dfrac{4}{3} j = 120$ $j = \dfrac{3}{4} \cdot 120 = 90$.